Question

sakuras house is at an elevation between 113 m and 120 m above sea level. her friend ted lives about 15 m below her.

part a
choose the compound inequality that describes the elevation ( x ) of ted’s house

• a. ( 113 leq 15 - x leq 120 )
• b. ( 113 leq x + 15 leq 120 )
• c. ( 113 leq x leq 120 )
• d. ( 113 leq x - 15 leq 120 )

part b
ted lives between (\boxed{}) m and (\boxed{}) m above sea level.

Explanation:

Part A

Step1: Analyze the relationship

Sakura's elevation (let's call it \( y \)) is between 113 m and 120 m, so \( 113 \leq y \leq 120 \). Ted's elevation is \( x \), and he lives 15 m below Sakura, so \( y = x + 15 \).

Step2: Substitute \( y \)

Substitute \( y = x + 15 \) into the inequality for \( y \): \( 113 \leq x + 15 \leq 120 \). This matches option B.

Step1: Solve the inequality

We have \( 113 \leq x + 15 \leq 120 \). Subtract 15 from all parts: \( 113 - 15 \leq x \leq 120 - 15 \).

Step2: Calculate the values

\( 113 - 15 = 98 \) and \( 120 - 15 = 105 \). So \( 98 \leq x \leq 105 \).

Answer:

B. \( 113 \leq x + 15 \leq 120 \)

Part B